Adhesively-bonded Patch Repair with Composites

Adhesively-bonded composite patch repairs over cracked or corrosion-damaged metallic aircraft structures have shown great promise for extending life of ageing structures. This study presents the numerical investigation into the interface behaviour of adhesively-bonded cracked aluminum alloy substrate patched with fibre-reinforced composite material. The adhesive is modelled as an elasto-plastic bilinear material to characterise the debond behaviour, while the defective substrate is regarded as linear elastic continuum. Two typical patch shapes were selected based on information available in the literature. Geometric and material nonlinear analyses for square and octagonal patches were performed to capture peel and shear stresses developed between the substrate and the patch to examine the possibility of interface delamination/debonding. Parametric studies on adhesive thickness and patch thickness were carried out to predict their infuence on damage tolerance of repaired structures.

Long-range synthon Aufbau modules (LSAM) in crystal structures: systematic changes in C6H6-nFn (0 <= n <= 6) fluorobenzenes

We discuss the assembly of a three-dimensional molecular crystal in terms of short-range supramolecular synthons that spontaneously organize themselves according to Aufbau principles into long-range geometries characteristic of the molecules themselves. For this purpose we have examined the systematic changes in the known crystal structures of a family of fluorobenzenes, C6H6-nFn, where 0 <= n <= 6. Crystal assembly is initiated by forming long-range synthon Aufbau modules (LSAM) that carry the imprint of the synthons. For example, when 1 <= n <= 5 the short-range synthons use H center dot center dot center dot F interactions to form the LSAMs. In the n = 0 and n = 6 compounds, the synthons are H center dot center dot center dot C and F center dot center dot center dot C interactions, respectively. The LSAMs are usually one-dimensional. In this study we show that these 1D LSAMs assemble into 2D quasi-hexagonal close-packed layers. The 3D crystal structure is obtained from the various kinds of close-packing known for these 2D layers. The final stages of this 1D -> 2D -> 3D assembly seem to be more influenced by the packing of LSAMs than by any other factor. In these final stages, there may not be so much influence exerted by the stronger short-range synthons. We discuss the evolution of these fluorobenzene crystal structures in terms of putative LSAMs and the purely geometric relationships between the n and (6 - n) compounds that can thus be expected. Such particle-hole pairs show structural similarities. Our discussion is quantified by the interpretation of intermolecular distances in terms of atomic sizes and with qualitative predictions of magnetic model systems.

Long-range synthon Aufbau modules (LSAM) in crystal structures: systematic changes in C6H6-nFn (0 <= n <= 6) fluorobenzenes

We discuss the assembly of a three-dimensional molecular crystal in terms of short-range supramolecular synthons that spontaneously organize themselves according to Aufbau principles into long-range geometries characteristic of the molecules themselves. For this purpose we have examined the systematic changes in the known crystal structures of a family of fluorobenzenes, C6H6-nFn, where 0 <= n <= 6. Crystal assembly is initiated by forming long-range synthon Aufbau modules (LSAM) that carry the imprint of the synthons. For example, when 1 <= n <= 5 the short-range synthons use H center dot center dot center dot F interactions to form the LSAMs. In the n = 0 and n = 6 compounds, the synthons are H center dot center dot center dot C and F center dot center dot center dot C interactions, respectively. The LSAMs are usually one-dimensional. In this study we show that these 1D LSAMs assemble into 2D quasi-hexagonal close-packed layers. The 3D crystal structure is obtained from the various kinds of close-packing known for these 2D layers. The final stages of this 1D -> 2D -> 3D assembly seem to be more influenced by the packing of LSAMs than by any other factor. In these final stages, there may not be so much influence exerted by the stronger short-range synthons. We discuss the evolution of these fluorobenzene crystal structures in terms of putative LSAMs and the purely geometric relationships between the n and (6 - n) compounds that can thus be expected. Such particle-hole pairs show structural similarities. Our discussion is quantified by the interpretation of intermolecular distances in terms of atomic sizes and with qualitative predictions of magnetic model systems.

On Using Projective Relations for Calibration and Estimation in a Structured-Light Scanner

For structured-light scanners, the projective geometry between a projector-camera pair is identical to that of a camera-camera pair. Consequently, in conjunction with calibration, a variety of geometric relations are available for three-dimensional Euclidean reconstruction. In this paper, we use projector-camera epipolar properties and the projective invariance of the cross-ratio to solve for 3D geometry. A key contribution of our approach is the use of homographies induced by reference planes, along with a calibrated camera, resulting in a simple parametric representation for projector and system calibration. Compared to existing solutions that require an elaborate calibration process, our method is simple while ensuring geometric consistency. Our formulation using the invariance of the cross-ratio is also extensible to multiple estimates of 3D geometry that can be analysed in a statistical sense. The performance of our system is demonstrated on some cultural artifacts and geometric surfaces.

On the compactness of isometry groups in complex analysis

We prove that the group of continuous isometries for the Kobayashi or Caratheodory metrics of a strongly convex domain in C-n is compact unless the domain is biholomorphic to the ball. A key ingredient, proved using differential geometric ideas, is that a continuous isometry between a strongly convex domain and the ball has to be biholomorphic or anti-biholomorphic. Combining this with a metric version of Pinchuk's rescaling technique gives the main result.

Inverted V-Notch: Practical Proportional Weir

This paper presents a practical linear proportional weir of simple geometric shape in the form of an inverted V-notch or inward trapezium. The flow through this weir, of half-width w and altitude d, for depths above 0.22d is proportional to the depth of flow measured above a reference plane situated at 0.08d for all heads in the range 0.22d<=h<=0.94d, with a maximum percentage deviation of ±1.5 from the theoretical discharge. The linear relationship between head and discharge is based on numerical optimization procedures. Nearly 75% of the depth of inverted V-notch can be used effectively as the measuring range. Experiments with four weirs, with different vertex angles, show excellent agreement with the theory by giving an average coefficient of discharge for each weir varying from 0.61–0.62.

Behaviour of Bi-adhesive Joints

The use of relatively low modulus adhesive at the ends of overlap in a bi-adhesive bondline of a bonded joint can reduce the stress concentration significantly and, therefore, potentially lead to higher strength of the joint. This study presents the two-dimensional and three-dimensional nonlinear (geometric and material) finite element analyses of adhesively bonded single lap joints having modulus-graded bondline under monotonic loading conditions. The adhesives were modelled as an elasto-plastic multi-linear material, while the substrates were regarded as both linear elastic and bi-linear elasto-plastic material. The computational simulations have been performed to investigate the bondline behaviour by studying the stress and strain distributions both at the mid-plane as well as at the interface of the bondline. It has been observed that the static strength is higher for joints with bi-adhesive bondlines compared to those with single adhesives in bondline. Higher joint strength has also been observed for optimum bi-adhesive bondline ratio through parametric studies. Effects of load level, and bondline thickness on stress distribution in the bi-adhesive bondline have also been studied. 3D analysis results reveal the existence of complex multi-axial stress/strain state at the ends of the overlap in the bondline which cannot be observed in 2D plane strain analysis. About 1/3rd of the width of the joint from the free edge in the width direction has 3D stress state, especially in the compliant adhesive of the bondline. Magnitudes of longitudinal and lateral stress/strain components are comparable to peel stress/strain components. It has also been analytically shown that the in-plane global stiffness of the joint remains unaffected by modulus gradation of the bondline adhesive. (C) Koninklijke Brill NV, Leiden, 2010.

Adhesively-bonded Patch Repair with Composites

Adhesively-bonded composite patch repairs over cracked or corrosion-damaged metallic aircraft structures have shown great promise for extending life of ageing structures. This study presents the numerical investigation into the interface behaviour of adhesively-bonded cracked aluminum alloy substrate patched with fibre-reinforced composite material. The adhesive is modelled as an elasto-plastic bilinear material to characterise the debond behaviour, while the defective substrate is regarded as linear elastic continuum. Two typical patch shapes were selected based on information available in the literature. Geometric and material nonlinear analyses for square and octagonal patches were performed to capture peel and shear stresses developed between the substrate and the patch to examine the possibility of interface delamination/debonding. Parametric studies on adhesive thickness and patch thickness were carried out to predict their infuence on damage tolerance of repaired structures.

Magnetization and magnetoresistive response of LiMn2O4 near the charge ordering transition

We report magnetization and magnetoresistance studies of the geometrically frustrated spinel compound LiMn2O4 near its charge ordering temperature. The effect of a 7 T magnetic field is to very slightly shift the transition in the resistivity to lower temperatures resulting in large negative magnetoresistance with significant hysteresis. This hysteresis is not reflected in the magnetization. These observations are compared with what is found in the colossal magnetoresistance and charge ordering perovskite manganese oxides. The manner in which geometric frustration influences the coupling of charge and spin degrees of freedom is examined.

A New Approach to 2-Asummability Testing

A relationship between 2-monotonicity and 2-asummability has been established and thereby a fast method for testing 2-asummability of switching functions derived. The approach is based on the fact that only a particular type of 2-sums need be examined for 2-asummability testing of 2-monotonic switching functions. These 2-sums are those which contain more than five 1's. 2-asummability testing for these 2-sums can be easily done by using the authors' technique.

A note on the Berry phase for systems having one degree of freedom

A one-dimensional arbitrary system with quantum Hamiltonian H(q, p) is shown to acquire the 'geometric' phase gamma (C)=(1/2) contour integral c(Podqo-qodpo) under adiabatic transport q to q+q+qo(t) and p to p+po(t) along a closed circuit C in the parameter space (qo(t), po(t)). The non-vanishing nature of this phase, despite only one degree of freedom (q), is due ultimately to the underlying non-Abelian Weyl group. A physical realisation in which this Berry phase results in a line spread is briefly discussed.

Steady flow of couple stress fluid through tubes of slowly varying cross-sections--application to blood flows

Steady laminar flow of a non-Newtonian fluid based on couple stress fluid theory, through narrow tubes of varying cross-sections has been studied theoretically. Asymptotic solutions are obtained for the basic equations and the expressions for the velocity field and the wall shear stress are derived for a general cross-section. Computation and discussions are carried out for the geometries which occur in the context of physiological flows or in particular blood flows. The tapered tubes and constricted tubes are of special importance. It is observed that increase in certain parameters results in erratic flow behaviour proximal to the constricted areas which is further enhanced by the increase in the geometric parameters. This elucidates the implications of the flow in the development of vascular lesions.

Efficient algorithms for domination and Hamilton circuit problems on permutation graphs

The domination and Hamilton circuit problems are of interest both in algorithm design and complexity theory. The domination problem has applications in facility location and the Hamilton circuit problem has applications in routing problems in communications and operations research.The problem of deciding if G has a dominating set of cardinality at most k, and the problem of determining if G has a Hamilton circuit are NP-Complete. Polynomial time algorithms are, however, available for a large number of restricted classes. A motivation for the study of these algorithms is that they not only give insight into the characterization of these classes but also require a variety of algorithmic techniques and data structures. So the search for efficient algorithms, for these problems in many classes still continues.A class of perfect graphs which is practically important and mathematically interesting is the class of permutation graphs. The domination problem is polynomial time solvable on permutation graphs. Algorithms that are already available are of time complexity O(n2) or more, and space complexity O(n2) on these graphs. The Hamilton circuit problem is open for this class.We present a simple O(n) time and O(n) space algorithm for the domination problem on permutation graphs. Unlike the existing algorithms, we use the concept of geometric representation of permutation graphs. Further, exploiting this geometric notion, we develop an O(n2) time and O(n) space algorithm for the Hamilton circuit problem.

An accurate numerical integration scheme for finite rotations using rotation vector parametrization

A numerical integration procedure for rotational motion using a rotation vector parametrization is explored from an engineering perspective by using rudimentary vector analysis. The incremental rotation vector, angular velocity and acceleration correspond to different tangent spaces of the rotation manifold at different times and have a non-vectorial character. We rewrite the equation of motion in terms of vectors lying in the same tangent space, facilitating vector space operations consistent with the underlying geometric structure. While any integration algorithm (that works within a vector space setting) may be used, we presently employ a family of explicit Runge-Kutta algorithms to solve this equation. While this work is primarily motivated out of a need for highly accurate numerical solutions of dissipative rotational systems of engineering interest, we also compare the numerical performance of the present scheme with some of the invariant preserving schemes, namely ALGO-C1, STW, LIEMIDEA] and SUBCYC-M. Numerical results show better local accuracy via the present approach vis-a-vis the preserving algorithms. It is also noted that the preserving algorithms do not simultaneously preserve all constants of motion. We incorporate adaptive time-stepping within the present scheme and this in turn enables still higher accuracy and a `near preservation' of constants of motion over significantly longer intervals. (C) 2010 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

Application of novel method for surface-ray tracing over hyperboloidal scatterers

A novel geodesic constant method has been developed for the hitherto unsolved problem of surface-ray tracing over a class of surface, namely the general hyperboloid of revolution (GHOR). All the ray-geometric parameters are obtained analytically in a one-parameter form. The ray parameters derived here for the first time can be readily used in the UTD formulation for computing the mutual coupling between the antennas located on the GHOR.